Abstract

We first report Fourier analyses of a collection of 348 daylight spectral power distributions and 1695 biochrome surface reflectance functions. The power spectra of the daylights are low pass with more than 99% of spectral power below 1 cycle/300 nm and 99.9% below 3 cycles/300 nm. The power spectra of reflectance functions are also low pass with more than 99% of spectral power below 4 cycles/300 nm and 99.9% below 11 cycles/300 nm. Consequently, the resulting color signals are typically low pass with, for our samples, an estimated frequency cutoff of 5 cycles/300 nm. Theoretical and experimental data concerning human chromatic response in the frequency domain show that this limit corresponds to the highest frequency that the color system can resolve. The implications for normal and abnormal human color vision are discussed.

© 2000 Optical Society of America

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  1. Biochrome surfaces include two categories of biological colorations that involve two different processes: pigmentary colors result from selective absorption of light by pigments, and schemochrome colors result from selective reflection of light by scattering, interference, or diffraction. See Ref. 13 below.
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    [Crossref]
  15. Note that the two last terms correspond to the terms “comb-filtered-spectra” and “comb-frequency” introduced by Barlow (Ref. 18 below). Comb-filtered spectra are sinusoidal spectral modulations analogous to spatial-frequency gratings used to determine the contrast sensitivity function of the visual system in the spatial domain.
  16. The natural unit for the F power density spectrum of a spectral reflectance function plotted against wavelength in nanometers is cycles/nanometer. The resulting numbers are small and difficult to interpret. As we are concerned mainly with the human visible spectrum, we report results for F power density spectra of spectral reflectance functions in units of cycles/300 nm, cycles across a nominal human visible spectrum.
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
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  23. L. Chittka, R. Menzel, “The evolutionary adaptation of flower colors and the insect pollinators’ color vision system,” J. Comp. Physiol. A 171, 171–181 (1992).
    [Crossref]
  24. B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
    [Crossref]
  25. A first analysis performed on each of the data collections (results not shown) indicates that 0.985 to 0.998 of the relative energy falls below at 6 c/300 nm. High F frequencies due to noise in the spectral measurements may have led us to underestimate the amount of energy recovered at this limit. A second set of values was computed from the mean cumulative F power density spectra truncated at 15 c/300 nm. Furthermore, in order to discount the possibility that the higher F-frequency cutoff is somehow introduced by including the near-ultraviolet spectrum in the analyses, we used only data from 400–700 nm in the analyses.
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    [Crossref]
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    [Crossref] [PubMed]
  28. The letters S-, M-, and L- refer to the short-, medium-, and long-wavelength cone fundamentals.
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    [Crossref] [PubMed]
  30. This resolution is obtained by extending the SSR function to 3000 points on the short-wavelength side.
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    [Crossref] [PubMed]
  32. J. Romero, L. Jiménez del Barco, E. Hita, “Mathematical reconstruction of color-matching functions,” J. Opt. Soc. Am. A 9, 25–29 (1992).
    [Crossref]
  33. V. Bonnardel, E. M. Valero, “Discrimination ellipses of deuteranomalous observers plotted in a personalised color diagram,” Perception 28, 70 (1999).
  34. J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
    [Crossref]
  35. The Weber fraction for the three classes of receptors (L, M, S) are computed for F frequencies varying from 0.1 to 6 c (0.1 c) step and for phase from 0 to 330° (with 30° steps). For each phase the value for the optimal phase only is plotted.
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    [PubMed]
  37. A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
  40. J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
    [Crossref] [PubMed]
  41. C. R. Ingling, B. H.-P. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977).
    [Crossref] [PubMed]
  42. The notation [L + M]-S refers to a hypothetical mechanism whose excitation is a linear combination of L-, M-, and S-cone excitations: 0.24L+0.11M-0.7S. The mechanism [L + S]-M is defined by 1.2L+0.4S-1.6M and the mechanism [L-M] by 1.2L-1.6M.
  43. C. R. Ingling, “The spectral sensitivity of the opponent-color channels,” Vision Res. 17, 1083–1089 (1977).
    [Crossref] [PubMed]
  44. The response SM(f, p) of a mechanism M for a given phase p and frequency f is computed for a maximal modulation. T. Benzschawel, M. H. Brill, T. E. Cohn, “Analysis of human color mechanisms using sinusoidal spectral power distributions,” J. Opt. Soc. Am. A 3, 1713–1725 (1986).
    [Crossref] [PubMed]
  45. H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
    [Crossref]
  46. H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
    [Crossref]
  47. T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
    [PubMed]
  48. A. Chapanis, “Spectral saturation and its relation to color-vision defects,” J. Exp. Psychol. 34, 24–44 (1944);B. C. Regan, J. P. Reffin, J. D. Mollon, “Luminance noise and the rapid determination of discrimination ellipses in color deficiency,” Vision Res. 34, 24–44 (1994).
    [Crossref]
  49. P. DeMarco, J. Pokorny, V. C. Smith, “Full-spectrum cone come sensitivity functions for X-chromosome-linked anomalous trichromats,” J. Opt. Soc. Am. A 9, 1465–1476 (1992).
    [Crossref] [PubMed]
  50. This claim is evident if one recalls that the basis elements of a linear model can be thought of as vectors in a possibly infinite-dimensional vector space. A linear model represents all of the vectors in a subspace spanned by its basis elements. If there are two subspaces, each of dimension N, then the smallest subspace that contains both of them has a dimension no smaller than N (if the two subspaces were in fact one and the same) and no greater than 2N (when the intersection of the two subspaces is the zero vector). See P. R. Halmos, Finite-Dimensional Vector Spaces (Springer Verlag, New York, 1974), Sec. 12.
  51. T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
    [Crossref]
  52. R. Lenz, M. Österberg, J. Hiltunen, T. Jaaskelainen, J. Parkkinen, “Unsupervised filtering of color spectra,” J. Opt. Soc. Am. A 13, 1315–1324 (1996).
    [Crossref]
  53. We assume that there is only one illuminant in the scene and ignore the possibility of interreflections among surfaces within the scene. See the discussion of “flat-world” assumptions in Ref. 2.
  54. G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colors coding and optimum color information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
    [Crossref]

1999 (1)

V. Bonnardel, E. M. Valero, “Discrimination ellipses of deuteranomalous observers plotted in a personalised color diagram,” Perception 28, 70 (1999).

1998 (1)

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

1997 (3)

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[Crossref]

J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[Crossref]

J. Romero, A. Garcia-Beltran, J. Hernandez-Andres, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[Crossref]

1996 (4)

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
[PubMed]

R. Lenz, M. Österberg, J. Hiltunen, T. Jaaskelainen, J. Parkkinen, “Unsupervised filtering of color spectra,” J. Opt. Soc. Am. A 13, 1315–1324 (1996).
[Crossref]

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[Crossref] [PubMed]

L. Chittka, “Optimal sets of color receptors and color opponent systems for coding of natural objects in insect vision,” J. Theor. Biol. 181, 179–196 (1996).
[Crossref]

1994 (2)

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

1993 (1)

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for color vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[Crossref]

1992 (3)

1990 (1)

1989 (2)

J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
[Crossref]

J. D. Mollon, “‘Tho’ she kneel’d in that place where they grew…’,” J. Exp. Biol. 146, 21–38 (1989).
[PubMed]

1986 (3)

1984 (2)

1983 (3)

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
[Crossref]

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colors coding and optimum color information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[Crossref]

1982 (2)

J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[Crossref] [PubMed]

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[Crossref] [PubMed]

1979 (2)

1977 (3)

C. R. Ingling, B. H.-P. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977).
[Crossref] [PubMed]

C. R. Ingling, “The spectral sensitivity of the opponent-color channels,” Vision Res. 17, 1083–1089 (1977).
[Crossref] [PubMed]

W. S. Stiles, G. Wyszecki, N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,” J. Opt. Soc. Am. 67, 779–784 (1977).
[Crossref]

1975 (1)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigment between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

1964 (2)

1963 (1)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 130, 35–44 (1963).

1955 (1)

1944 (1)

A. Chapanis, “Spectral saturation and its relation to color-vision defects,” J. Exp. Psychol. 34, 24–44 (1944);B. C. Regan, J. P. Reffin, J. D. Mollon, “Luminance noise and the rapid determination of discrimination ellipses in color deficiency,” Vision Res. 34, 24–44 (1994).
[Crossref]

1943 (1)

Barlow, H. B.

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[Crossref] [PubMed]

Bellemare, H.

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[Crossref] [PubMed]

Benzschawel, T.

Berendschot, T. T. J. M.

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
[PubMed]

Bonnardel, V.

V. Bonnardel, E. M. Valero, “Discrimination ellipses of deuteranomalous observers plotted in a personalised color diagram,” Perception 28, 70 (1999).

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[Crossref] [PubMed]

Bowmaker, J. K.

H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
[Crossref]

Boynton, R. M.

Bracewell, R.

R. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1965).

Brill, M. H.

Buchsbaum, G.

Campbell, F. W.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 130, 35–44 (1963).

Chapanis, A.

A. Chapanis, “Spectral saturation and its relation to color-vision defects,” J. Exp. Psychol. 34, 24–44 (1944);B. C. Regan, J. P. Reffin, J. D. Mollon, “Luminance noise and the rapid determination of discrimination ellipses in color deficiency,” Vision Res. 34, 24–44 (1994).
[Crossref]

Charles-Dominique, P.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

Chittka, L.

L. Chittka, “Optimal sets of color receptors and color opponent systems for coding of natural objects in insect vision,” J. Theor. Biol. 181, 179–196 (1996).
[Crossref]

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

L. Chittka, R. Menzel, “The evolutionary adaptation of flower colors and the insect pollinators’ color vision system,” J. Comp. Physiol. A 171, 171–181 (1992).
[Crossref]

Cohen, J.

J. Cohen, “Dependency of spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
[Crossref]

Cohn, T. E.

Dartnall, H. J.

H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
[Crossref]

del Barco, L. Jiménez

DeMarco, P.

Derrington, A. M.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Garcia, J. A.

J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[Crossref]

Garcia-Beltran, A.

Gemperlein, R.

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

Gershon, R.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Gibson, K. S.

Gottschalk, A.

Hallikainen, J.

Halmos, P. R.

This claim is evident if one recalls that the basis elements of a linear model can be thought of as vectors in a possibly infinite-dimensional vector space. A linear model represents all of the vectors in a subspace spanned by its basis elements. If there are two subspaces, each of dimension N, then the smallest subspace that contains both of them has a dimension no smaller than N (if the two subspaces were in fact one and the same) and no greater than 2N (when the intersection of the two subspaces is the zero vector). See P. R. Halmos, Finite-Dimensional Vector Spaces (Springer Verlag, New York, 1974), Sec. 12.

Heely, D. W.

J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[Crossref] [PubMed]

Hernandez-Andres, J.

Hiltunen, J.

Hita, E.

Hurvich, L. M.

Ingling, C. R.

C. R. Ingling, B. H.-P. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977).
[Crossref] [PubMed]

C. R. Ingling, “The spectral sensitivity of the opponent-color channels,” Vision Res. 17, 1083–1089 (1977).
[Crossref] [PubMed]

Iwan, L. S.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Jaaskelainen, T.

Jameson, D.

Judd, D. B.

Julliot, C.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

Kelley, K. L.

Krauskopf, J.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[Crossref] [PubMed]

Krinov, E. L.

E. L. Krinov, Spectral Reflectance Properties of Natural Formations, (National Research Council of Canada, Ottawa, 1947).

Lennie, P.

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

Lenz, R.

MacAdam, D. L.

MacLeod, D. I. A.

Maloney, L. T.

Menzel, R.

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

L. Chittka, R. Menzel, “The evolutionary adaptation of flower colors and the insect pollinators’ color vision system,” J. Comp. Physiol. A 171, 171–181 (1992).
[Crossref]

Mollon, J. D.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[Crossref]

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[Crossref] [PubMed]

J. D. Mollon, “‘Tho’ she kneel’d in that place where they grew…’,” J. Exp. Biol. 146, 21–38 (1989).
[PubMed]

H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
[Crossref]

Nassau, K.

K. Nassau, The Physics and Chemistry of Color: The Fifteen Causes of Color (Wiley, New York, 1983).

Nickerson, D.

Nieves, J. L.

J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[Crossref]

Ohta, N.

Österberg, M.

Parkkinen, J.

Parkkinen, J. P. S.

Paul, R.

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

Pokorny, J.

Regan, B. C.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

Robson, J. G.

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 130, 35–44 (1963).

Romero, J.

Shmida, A.

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

Simmen, B.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

Smith, V. C.

Steiner, A.

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

Stiles, W. S.

Toyooka, S.

Troje, N.

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

Tsou, B. H.-P.

C. R. Ingling, B. H.-P. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977).
[Crossref] [PubMed]

Valero, E.

J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[Crossref]

Valero, E. M.

V. Bonnardel, E. M. Valero, “Discrimination ellipses of deuteranomalous observers plotted in a personalised color diagram,” Perception 28, 70 (1999).

van de Kraats, J.

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
[PubMed]

van Hateren, J. H.

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for color vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[Crossref]

van Norren, D.

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
[PubMed]

Vienot, F.

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

Vrhel, M. J.

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

Wandel, B. A.

Webster, M. A.

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[Crossref]

Werner, J. S.

Williams, D. R.

J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[Crossref] [PubMed]

Wooten, B. R.

Wyszecki, G.

Color Res. Appl. (1)

M. J. Vrhel, R. Gershon, L. S. Iwan, “Measurement and analysis of object reflectance spectra,” Color Res. Appl. 19, 4–9 (1994).

J. Comp. Physiol. A (1)

L. Chittka, R. Menzel, “The evolutionary adaptation of flower colors and the insect pollinators’ color vision system,” J. Comp. Physiol. A 171, 171–181 (1992).
[Crossref]

J. Exp. Biol. (1)

J. D. Mollon, “‘Tho’ she kneel’d in that place where they grew…’,” J. Exp. Biol. 146, 21–38 (1989).
[PubMed]

J. Exp. Psychol. (1)

A. Chapanis, “Spectral saturation and its relation to color-vision defects,” J. Exp. Psychol. 34, 24–44 (1944);B. C. Regan, J. P. Reffin, J. D. Mollon, “Luminance noise and the rapid determination of discrimination ellipses in color deficiency,” Vision Res. 34, 24–44 (1994).
[Crossref]

J. Opt. (Paris) (1)

J. Romero, J. A. Garcia, E. Valero, J. L. Nieves, “Measurements of the spectral modulation sensitivity function for two normal observers with CRT monitors,” J. Opt. (Paris) 28, 190–198 (1997).
[Crossref]

J. Opt. Soc. Am. (6)

D. I. A. MacLeod, R. M. Boynton, “Chromaticity diagram showing cone excitation by stimuli of equal luminance,” J. Opt. Soc. Am. 69, 1183–1186 (1979).
[Crossref] [PubMed]

D. B. Judd, D. L. MacAdam, G. Wyszecki, “Spectral distribution of typical daylight as a function of correlated color temperature,” J. Opt. Soc. Am. 54, 1031–1040 (1964); S. R. Das, V. D. P. Sastri, “Spectral distribution and color of tropical daylight,” J. Opt. Soc. Am. 55, 319–323 (1965); V. D. P. Sastri, S. R. Das, “Spectral distribution and color of north sky at Delhi,” J. Opt. Soc. Am. 56, 829–830 (1966); V. D. P. Sastri, S. R. Das, “Typical spectra distributions and color for tropical daylight,” J. Opt. Soc. Am. 58, 391–398 (1968); E. R. Dixon, “Spectral distribution of Australian daylight,” J. Opt. Soc. Am. 68, 437–450 (1978).
[Crossref]

W. S. Stiles, G. Wyszecki, N. Ohta, “Counting metameric object-color stimuli using frequency-limited spectral reflectance functions,” J. Opt. Soc. Am. 67, 779–784 (1977).
[Crossref]

K. L. Kelley, K. S. Gibson, D. Nickerson, “Tristimulus specification of the Munsell Book of Color from spectrophotometric measurements,” J. Opt. Soc. Am. 33, 355–376 (1943).
[Crossref]

L. M. Hurvich, D. Jameson, “Some quantitative aspects of an opponent-colors theory. I. Chromatic responses and spectral saturation,” J. Opt. Soc. Am. 45, 546–552 (1955); L. M. Hurvich, D. Jameson, “Some quantitative aspects of an opponent-colors theory. II. Brightness, saturation, and hue in normal and dichromatic vision,” J. Opt. Soc. Am. 45, 602–616 (1955).
[Crossref] [PubMed]

J. S. Werner, B. R. Wooten, “Opponent-chromatic mechanisms: relation to photopigments and hue naming,” J. Opt. Soc. Am. 69, 422–434 (1979); S. Takahasi, Y. Ejima, M. Akita, “Effect of light adaptation on the perceptual red–green and yellow–blue opponent-color responses,” J. Opt. Soc. Am. A 2, 705–712 (1985); K. Shinomori, L. Spillmann, J. S. Werner, “S-cone signals to temporal OFF-channels: asymmetrical connections to postreceptoral chromatic mechanisms,” Vision Res. 39, 39–49 (1999).
[Crossref] [PubMed]

J. Opt. Soc. Am. A (10)

The response SM(f, p) of a mechanism M for a given phase p and frequency f is computed for a maximal modulation. T. Benzschawel, M. H. Brill, T. E. Cohn, “Analysis of human color mechanisms using sinusoidal spectral power distributions,” J. Opt. Soc. Am. A 3, 1713–1725 (1986).
[Crossref] [PubMed]

P. DeMarco, J. Pokorny, V. C. Smith, “Full-spectrum cone come sensitivity functions for X-chromosome-linked anomalous trichromats,” J. Opt. Soc. Am. A 9, 1465–1476 (1992).
[Crossref] [PubMed]

T. Jaaskelainen, J. Parkkinen, S. Toyooka, “Vector-subspace model for color representation,” J. Opt. Soc. Am. A 7, 725–730 (1990).
[Crossref]

R. Lenz, M. Österberg, J. Hiltunen, T. Jaaskelainen, J. Parkkinen, “Unsupervised filtering of color spectra,” J. Opt. Soc. Am. A 13, 1315–1324 (1996).
[Crossref]

L. T. Maloney, “Evaluation of linear models of surface spectral reflectance with small numbers of parameters,” J. Opt. Soc. Am. A 3, 1673–1681 (1986).
[Crossref] [PubMed]

J. P. S. Parkkinen, J. Hallikainen, T. Jaaskelainen, “Characteristic spectra of Munsell colors,” J. Opt. Soc. Am. A 6, 318–322 (1989).
[Crossref]

L. T. Maloney, B. A. Wandel, “Color constancy: a method for recovering surface spectral reflectance,” J. Opt. Soc. Am. A 3, 29–33 (1986).
[Crossref] [PubMed]

J. Romero, A. Garcia-Beltran, J. Hernandez-Andres, “Linear bases for representation of natural and artificial illuminants,” J. Opt. Soc. Am. A 14, 1007–1014 (1997).
[Crossref]

G. Buchsbaum, A. Gottschalk, “Chromaticity coordinates of frequency-limited functions,” J. Opt. Soc. Am. A 1, 885–887 (1984); G. Buchsbaum, “Chromaticity coordinates of frequency-limited functions: erratum,” J. Opt. Soc. Am. A 2, 95 (1985).
[Crossref] [PubMed]

J. Romero, L. Jiménez del Barco, E. Hita, “Mathematical reconstruction of color-matching functions,” J. Opt. Soc. Am. A 9, 25–29 (1992).
[Crossref]

J. Physiol. (3)

F. W. Campbell, J. G. Robson, “Application of Fourier analysis to the visibility of gratings,” J. Physiol. 130, 35–44 (1963).

T. T. J. M. Berendschot, J. van de Kraats, D. van Norren, “Foveal cone mosaic and visual pigment density in dichromats,” J. Physiol. 492, 307–314 (1996).
[PubMed]

H. B. Barlow, R. Gemperlein, R. Paul, A. Steiner, “Human contrast sensitivity for comb-filtered spectra,” J. Physiol. 340, 50 (1983); V. Bonnardel, F. J. Varela, “A frequency view of color: measuring the human sensitivity to square-wave spectral power distributions,” Proc. R. Soc. London Ser. B 245, 165–171 (1991);Ref. 20; V. Bonnardel, D. L. Ruderman, H. B. Barlow, “A fast determination of the spectral modulation sensitivity function: a comparison between trichromats and deuteranopes,” in Color Vision Deficiencies XIII, C. R. Cavonius, ed., Vol. 59 of Documenta Ophthalmolgy Proceedings Series (Kluwer Academic, Dordrecht, the Netherlands, 1997); V. Bonnardel, E. M. Valero, H. B. Barlow, “S-cone input into the red–green opponent-color mechanism in a detection task,” Perception 27, 169 (1998).
[Crossref]

J. Physiol. (London) (1)

A. M. Derrington, J. Krauskopf, P. Lennie, “Chromatic mechanisms in lateral geniculate nucleus of macaque,” J. Physiol. (London) 357, 241–265 (1984).

J. Theor. Biol. (1)

L. Chittka, “Optimal sets of color receptors and color opponent systems for coding of natural objects in insect vision,” J. Theor. Biol. 181, 179–196 (1996).
[Crossref]

Perception (1)

V. Bonnardel, E. M. Valero, “Discrimination ellipses of deuteranomalous observers plotted in a personalised color diagram,” Perception 28, 70 (1999).

Proc. R. Soc. London Ser. B (3)

J. H. van Hateren, “Spatial, temporal and spectral pre-processing for color vision,” Proc. R. Soc. London Ser. B 251, 61–68 (1993).
[Crossref]

H. J. Dartnall, J. K. Bowmaker, J. D. Mollon, “Human visual pigments: microspectophotometry results from the eyes of seven persons,” Proc. R. Soc. London Ser. B 220, 115–130 (1983).
[Crossref]

G. Buchsbaum, A. Gottschalk, “Trichromacy, opponent colors coding and optimum color information transmission in the retina,” Proc. R. Soc. London Ser. B 220, 89–113 (1983).
[Crossref]

Psychon. Sci. (1)

J. Cohen, “Dependency of spectral reflectance curves of the Munsell color chips,” Psychon. Sci. 1, 369–370 (1964).
[Crossref]

Vision Res. (9)

V. C. Smith, J. Pokorny, “Spectral sensitivity of the foveal cone photopigment between 400 and 500 nm,” Vision Res. 15, 161–171 (1975).
[Crossref] [PubMed]

L. Chittka, A. Shmida, N. Troje, R. Menzel, “Ultraviolets as a component of flower reflections, and the color perception of hymenoptera,” Vision Res. 34, 1489–1508 (1994).
[Crossref] [PubMed]

V. Bonnardel, H. Bellemare, J. D. Mollon, “Measurements of human sensitivity to comb-filtered spectra,” Vision Res. 36, 2713–2720 (1996).
[Crossref] [PubMed]

B. C. Regan, C. Julliot, B. Simmen, F. Vienot, P. Charles-Dominique, J. D. Mollon, “Frugivory and color vision in Alouatta seniculus, a trichromatic plathyrrhine monkey,” Vision Res. 38, 3321–3329 (1998).
[Crossref]

H. B. Barlow, “What causes trichromacy? A theoretical analysis using comb-filtered spectra,” Vision Res. 22, 635–643 (1982).
[Crossref] [PubMed]

M. A. Webster, J. D. Mollon, “Adaptation and the color statistics of natural images,” Vision Res. 37, 3283–3298 (1997).
[Crossref]

C. R. Ingling, “The spectral sensitivity of the opponent-color channels,” Vision Res. 17, 1083–1089 (1977).
[Crossref] [PubMed]

J. Krauskopf, D. R. Williams, D. W. Heely, “Cardinal directions of color space,” Vision Res. 22, 1123–1131 (1982);R. G. Cole, T. Hine, W. McIlhagga, “Detection mechanisms in L-, M-, and S-cone contrast space,” J. Opt. Soc. Am. A 10, 38–51 (1993); M. J. Sankeralli, K. T. Mullen, “Estimation of the L-, M-, and S-cone weights of the postreceptoral detection mechanisms,” J. Opt. Soc. Am. A 13, 906–915 (1996).
[Crossref] [PubMed]

C. R. Ingling, B. H.-P. Tsou, “Orthogonal combination of the three visual channels,” Vision Res. 17, 1075–1082 (1977).
[Crossref] [PubMed]

Other (14)

The notation [L + M]-S refers to a hypothetical mechanism whose excitation is a linear combination of L-, M-, and S-cone excitations: 0.24L+0.11M-0.7S. The mechanism [L + S]-M is defined by 1.2L+0.4S-1.6M and the mechanism [L-M] by 1.2L-1.6M.

This claim is evident if one recalls that the basis elements of a linear model can be thought of as vectors in a possibly infinite-dimensional vector space. A linear model represents all of the vectors in a subspace spanned by its basis elements. If there are two subspaces, each of dimension N, then the smallest subspace that contains both of them has a dimension no smaller than N (if the two subspaces were in fact one and the same) and no greater than 2N (when the intersection of the two subspaces is the zero vector). See P. R. Halmos, Finite-Dimensional Vector Spaces (Springer Verlag, New York, 1974), Sec. 12.

We assume that there is only one illuminant in the scene and ignore the possibility of interreflections among surfaces within the scene. See the discussion of “flat-world” assumptions in Ref. 2.

A first analysis performed on each of the data collections (results not shown) indicates that 0.985 to 0.998 of the relative energy falls below at 6 c/300 nm. High F frequencies due to noise in the spectral measurements may have led us to underestimate the amount of energy recovered at this limit. A second set of values was computed from the mean cumulative F power density spectra truncated at 15 c/300 nm. Furthermore, in order to discount the possibility that the higher F-frequency cutoff is somehow introduced by including the near-ultraviolet spectrum in the analyses, we used only data from 400–700 nm in the analyses.

This resolution is obtained by extending the SSR function to 3000 points on the short-wavelength side.

The letters S-, M-, and L- refer to the short-, medium-, and long-wavelength cone fundamentals.

The Weber fraction for the three classes of receptors (L, M, S) are computed for F frequencies varying from 0.1 to 6 c (0.1 c) step and for phase from 0 to 330° (with 30° steps). For each phase the value for the optimal phase only is plotted.

Biochrome surfaces include two categories of biological colorations that involve two different processes: pigmentary colors result from selective absorption of light by pigments, and schemochrome colors result from selective reflection of light by scattering, interference, or diffraction. See Ref. 13 below.

L. T. Maloney, “Physics-based approaches to modeling surface color perception,” in Color Vision: From Genes to Perception, K. R. Gegenfurtner, L. T. Sharpe, eds. (Cambridge U. Press, Cambridge, UK, 1999).

E. L. Krinov, Spectral Reflectance Properties of Natural Formations, (National Research Council of Canada, Ottawa, 1947).

K. Nassau, The Physics and Chemistry of Color: The Fifteen Causes of Color (Wiley, New York, 1983).

Note that the two last terms correspond to the terms “comb-filtered-spectra” and “comb-frequency” introduced by Barlow (Ref. 18 below). Comb-filtered spectra are sinusoidal spectral modulations analogous to spatial-frequency gratings used to determine the contrast sensitivity function of the visual system in the spatial domain.

The natural unit for the F power density spectrum of a spectral reflectance function plotted against wavelength in nanometers is cycles/nanometer. The resulting numbers are small and difficult to interpret. As we are concerned mainly with the human visible spectrum, we report results for F power density spectra of spectral reflectance functions in units of cycles/300 nm, cycles across a nominal human visible spectrum.

R. Bracewell, The Fourier Transform and Its Application (McGraw-Hill, New York, 1965).

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Figures (5)

Fig. 1
Fig. 1

Cumulative F power density spectrum of the four categories of pigment colors and daylight illuminants compared with that of the Nickerson–Munsell chips and Krinov’s natural samples from Ref. 5.

Fig. 2
Fig. 2

(a) Chromaticity coordinates of the four categories of samples plotted in the CIE 1931 chromaticity diagram with the locus of maximum chroma of Munsell samples (taken from Ref. 31) for comparison. (b) The same data plotted in the MacLeod–Boynton diagram along with the elliptical contour of three F frequencies (obtained by varying phase from 0 to 360°, with maximal modulation). The cross corresponds to the locus of the equal-energy spectrum.

Fig. 3
Fig. 3

Chromaticity coordinates in the MacLeod–Boynton diagram of four SSR’s and the same SSR’s low-pass filtered at different limits from 1 to 6 c/300 nm. DE indicates the axes of the discrimination ellipse of a normal trichromatic observer (with the semiaxes a=0.0256 and b=0.0034) measured for a color center of L/[L + M] = 0.514 and S/[L + M] = 0.29.

Fig. 4
Fig. 4

SSR’s (continuous curves) of each of the four samples used in Fig. 3 compared with the same SSR’s low-pass filtered at 3 c/300 nm (dashed curves). Distances in the McLeod–Boynton chromaticity diagram between the low-pass filtered spectra and the samples are 0.0011 for the color flower, 0.0008 for the white flower, 0.0002 for the leaf, and 0.0087 for the fruit sample.

Fig. 5
Fig. 5

Response of the human chromatic system at various levels of description in the frequency domain. (a) Response of the Smith–Pokorny cone fundamentals,29 (b) response of the Ingling–Tsou channels,41 (c) SMSF’s of normal trichromatic and deuteranopic observers adapted from Ref. 45, (d) response of dichromatic opponent-color channels derived from the Ingling–Tsou channels.

Tables (1)

Tables Icon

Table 1 Proportion of Spectral Energy below the Frequency Limit (c/300 nm)a

Equations (3)

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Sσ(λ)=j=1NσjSj(λ),
Eϵ(λ)=i=1MϵiEi(λ).
g(λ)=c0+c1 cos(2πλ)+c2 sin(2πλ)+c3 cos(2π2λ)+c4 sin(2π2λ)++cn-2 cos(2πf0λ)+cn-1 sin(2πf0λ).

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